title: On Perrin-Riou's exponential map and reciprocity laws for (phi,Gamma)-modules
creator: Riedel, Andreas
subject: ddc-510
subject: 510 Mathematics
description: Let K / Q_p be a finite Galois extension and D a (phi,Gamma)-module over the Robba ring B and N_dR(D) its associated p-adic differential equation.     In the first part we give a generalization of the Bloch-Kato exponential map for D using continuous Galois-cohomology groups H^i(G_K, W(D)) for the B-pair W(D) associated to D. We construct a big exponential map Omega_D,h for cyclotomic extensions of K for D in the style of Perrin-Riou extending techniques of Berger, which interpolates the generalized Bloch-Kato exponential maps on the finite levels.    In the second part we extend two definitions for pairings on D and its dual D^*(1) (resp. on N_dR(D) and its dual N_dR(D^*(1))) and prove a generalization of the reciprocity law, which relates these pairings under the big exponential map.     Finally, we give some results on the determinant associated to Omega_D,h, and formulate an integral version of a determinant conjecture in the semi-stable case. Further, we define i-Selmer groups and show under certain hypothesis a torsion property.
date: 2013
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/14935/1/diss%20final.pdf
identifier: DOI:10.11588/heidok.00014935
identifier: urn:nbn:de:bsz:16-heidok-149359
identifier:   Riedel, Andreas  (2013) On Perrin-Riou's exponential map and reciprocity laws for (phi,Gamma)-modules.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/14935/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng